1. Field of the Invention
The present invention relates to a designing method of a photomask used in a lithography process for a semiconductor device, a method for predicting a pattern formed in the lithography process and a computer program product.
2. Description of the Related Art
In the photolithography step which is one of the manufacturing steps of a semiconductor device, an exposure device is used. Exposure light, for example, ArF excimer laser light, is illuminated on the photomask by use of the exposure device and an image of a mask pattern is reduced and projected onto the surface of a substrate which is coated with photosensitive resin (photoresist).
The exposure light illuminated on the photomask is diffracted by the mask pattern. The diffracted light passes through a projecting lens and is converged on the substrate. Then, an interference pattern which is called an optical image is formed near the surface of the substrate. The photoresist is exposed to light along the interference pattern.
A fine pattern is formed on the surface of the substrate by subjecting the exposed substrate to a developing process. The fine pattern forming technique is improved year by year. In recent years, a resist pattern with a dimension smaller than 130 nm can be formed.
In order to form the fine resist pattern, it is important to control the exposure light amount (exposure dose). The photoresist can be properly exposed to light by exposing light of proper light intensity and, as a result, a resist pattern of a desired dimension can be formed on the substrate.
A resist pattern of a desired dimension cannot be formed if the exposure light amount is excessively larger or smaller. If the resist pattern of the desired dimension is not formed, a semiconductor device manufactured via steps performed after the photolithography process is not correctly operated. As a result, the semiconductor device is treated as a faulty device.
Therefore, in the manufacturing process, the dimension of the resist pattern is measured by use of, for example, an electron microscope after the exposure step. If the dimension is not a desired value, the photoresist is removed and then the process is started again from the beginning of the photolithography step.
An area which is simultaneously exposed by use of the exposure device is a rectangular form having one side of several tens of mm. One or more semiconductor devices are formed in the above area (simultaneously exposed area). Therefore, it is necessary to set the dimension of the resist pattern to a desired value in the entire portion of the simultaneously exposed area.
Generally, various patterns such as densely crowded patterns and isolated patterns are contained in patterns which can be transferred by one exposure process. When patterns with a dimension which is equivalent to or smaller than the exposure light wavelength are formed, not all of the patterns can be formed with desired dimensions even if the shape of the mask pattern is made similar to the shape of the resist pattern to be formed. That is, even if the dimension of the mask pattern is set to a dimension calculated by dividing the dimension of the resist pattern by the reduction rate of the projecting lens, not all of the patterns can be formed with the desired dimension.
Therefore, for example, in order to form or finish the densely crowded patterns and isolated patterns to have the same resist dimension, the mask pattern designing dimension corresponding to the densely crowded patterns and the mask pattern designing dimension corresponding to the isolated patterns are respectively changed to mask pattern designing dimensions of values different from dimensions calculated by dividing the dimensions of the resist patterns by the reduction rate of the projecting lens. The amount of a change of the mask pattern designing dimension is called the mask bias. The resist finishing dimension can be adjusted by changing the mask bias according to the pattern types.
In the actual exposure device, a phenomenon wherein the amplitude of light is attenuated by different amounts depending on the paths through which the light passes (which is hereinafter referred to as a pupil transmission factor variation) occurs. This is caused by non-uniformity of an anti-reflection film of a lens configuring the projection optical system or a lowering in the transmission factor due to the thickness of the lens as is described in Jpn. Pat. Appln. KOKAI Publication No. H9-63943, for example.
If the paths for diffraction light in the projection optical system are different, generally, the angle of the diffraction light incident on the projection lens and the distance through which the diffraction light passes through the projection lens will be changed. Therefore, the transmission factor of the projection optical system is changed depending on the paths for the diffraction light. Particularly, in fused silica which is generally used as a lens material at present, the transparency thereof tends to become lower for light with the wavelength shorter than 200 nm as the wavelength becomes shorter. Therefore, the pupil transmission factor variation indicates a particularly large value in the ArF exposure device (the exposure light wavelength is 193 nm).
The paths through which diffraction lights pass are different depending on the mask patterns. Therefore, when the pupil transmission factor variation occurs in the projection lens, the transmission factor of the projection optical system receives different influences depending on the mask patterns. As a result, the optimum exposure light amount set to finish the resist pattern to a desired dimension is changed. In addition, the degree of the change becomes different depending on the pattern types, for example, between the densely crowded patterns and the isolated patterns.
Therefore, even when the mask biases of the respective patterns are designed to simultaneously finish the densely crowded patterns and the isolated patterns to desired dimensions, there occurs a possibility that the densely crowded patterns and the isolated patterns may not be simultaneously finished to the desired dimensions if the pupil transmission factor variation is not taken into consideration.
In order to prevent occurrence of the above problem in advance, a method for preparing in advance a plurality of photomasks having different mask biases and deriving optimum mask bias based on trial and error is considered. However, a relatively long time and high cost are required to realize the above method and the method cannot be used as a practical solution.
Further, in order to prevent an influence by the pupil transmission factor variation, a method for measuring the degree of a pupil variation rate of the projection optical system, predicting an optical image on a photosensitive substrate based on the result of measurement and designing a photomask to make the predicted optical image and the designed optical image coincident to each other is considered.
The measuring method of the degree of the pupil transmission variation rate is disclosed in Jpn. Pat. Appln. KOKAI Publication No. 2001-230179, for example. By carrying out the measuring method, the distribution of transmission factors in a plurality of points on a pupil coordinate system can be understood.
In the conventional measuring method, data of the pupil transmission factor variation is matrix data on a pupil plane. Therefore, when the pupil transmission factor variation varies in a complicated fashion on the pupil plane, the data amount which is required to be processed becomes extremely large. Therefore, an optical image predicting method carried out based on the measurement result of the conventional measuring method and the photomask designing method using the optical image predicting method cannot be used as practical methods.